Monthly Archives: March 2021

Dear Family, your Operation Maths guide to Decimals and Percentages

Dear Family, given below is a brief guide to understanding the topic of decimals and percentages, as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about decimals and percentages. The digital resources are organised according to approximate class level:

• Third and Fourth classes (Decimals only)
• Fifth and Sixth classes (Decimals and Percentages)

Understanding Decimals and Percentages

Decimals, or decimal fractions, to give them their full title, are fractions of a whole amount, where the whole has been divided into ten parts (tenths), a hundred parts (hundredths), a thousand parts (thousandths) etc. They are typically written using a decimal point. This means that an amount that is the same value may be describes as a fraction, as a decimal fraction and as both, e.g.:

1/2 (1 half) = 5/10 (5 tenths) = 0.5 = 50/100 (50 hundredths) = 0.50 etc

Percentages are very closely related to both fractions and decimals: per cent means out of 100, therefore an amount of percent is the same as that amount of hundredths, e.g.:

25% (twenty five percent) = 25 hundredths = 25/100 = 0.25

In Operation Maths, the children are first formally introduced to decimals (tenths only) in third class and then to hundredths in fourth class and thousandths in fifth class. The children are also introduced to percentages in fifths class. However, it is worth noting that the children would have informally explored decimals since being introduced to euro and cent in first class.

Since decimals are inherently linked with both fractions and the place value system, (also introduced in first class), the children’s understanding of decimals and percentages in the senior classes will build on this prior knowledge.

Practical Suggestions for Supporting Children

• Draw your child’s attention to decimals and percentages around your home and in the wider environment, e.g:
  • Decimals on products 1.5 litre bottle of water, 2.5 kg bag of dog food, petrol or diesel sold per litre as cents to tenths (e.g. 125.9c/litre)
  • Percentage discount: 20% off, 10% off, 50% extra free etc.
  • The percentage left for a device to fully charge or for a program/movie to fully download.
  • The percentage power left in the battery
  • Recorded times (as decimal fractions of a second) for races, etc.
• When you are talking about decimal numbers be careful to use the correct language e.g. for 23.05 say ‘twenty three point zero five’. (Remember: 0 is a digit called zero, whereas O or ‘oh’ is a letter of the alphabet and not a number at all! So, when verbalising numbers with zero, try to get into the habit of saying ‘zero’ instead of ‘oh’).

Digital Resources for Third and Fourth Classes

White Rose Maths – Decimals: a series of lessons, including Tenths as Decimals, Hundredths as Decimals, Writing Decimals, Comparing Decimals, Ordering Decimals and Rounding Decimals.

 

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Matholia – Decimals: A series of video lessons. Third class should focus on decimals to tenths, and fourth class on decimals to hundredths.

 

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Khan Academy – Decimals: in this video and the videos that follow, explore decimal fractions and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Happy Numbers – Decimal Fractions: A series of lessons and activities; scroll down to do Module 4 (Fourth Grade)

 

 

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Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself. 

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Caterpillar Ordering: Choose ordering to order numbers with tenths (1 decimal place)

 

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Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers up to 10, 1 decimal place or 2 decimal places or both.

 

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Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).

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Place Value Charts: Make a given number by combining the parts that make up the number. Select practice and then either T O . t (1 decimal place, for third class) or T O . t h (2 decimal places, for fourth class) in either column.

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Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

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Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the decimals game. 

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I Know It! – Decimals: Scroll down to Decimals (Third Grade) to do any of the activities with tenths (third class) and/or hundredths (fourth class). There are some more advanced decimal activities in the fourth grade section, both in the section on Numbers & Place Value and in the section on Fractions & Decimals. 

 

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Splash Learn – Decimals: An assortment of decimal games organised according to US grade levels; third classes could do the games that include tenths only and fourth classes could look at all the Fourth Grade games.

 

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That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals (choose decimal option on left hand side), Inequalities for comparing decimals and/or fractions and Reduce for converting decimals to an alternative form. 

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Decimals: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)  

Digital Resources for Fifth and Sixth Classes

White Rose Maths – Decimals & Percent: a series of lessons, including Decimals as Fractions, Thousandths, Rounding Decimals, Order & Compare Decimals, Percentages, Percentages as Fractions and Decimals, Adding Decimals 1, Adding Decimals 2, Subtracting Decimals 1, Subtracting Decimals 2, Multiplying Decimals,  and Dividing Decimals.

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Matholia – Decimals and Percentage:  A series of video lessons. For decimals, fifth and sixth classes should focus on the lessons involving decimals to thousandths (3 decimal places).

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Khan Academy – Decimal Place Value: explore decimal fractions in this series of lessons, and then answer the practice questions. If you wish, follow this up with Adding Decimals, Subtracting Decimals, Multiplying Decimals, Dividing Decimals or a series of lessons covering all Decimal Operations. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Khan Academy – Ratios, Rates and Percentages: Scroll down to the sections on percentages to explore them in this series of lessons, and then answer the practice questions. You can also register for a free Khan Academy account to record your progress and explore other topics. 

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Mashup Math: A collection of video lessons including Writing Decimals in Expanded Form, Converting Decimals to Fractions, Adding & Subtracting Decimals, Multiplying & Dividing Decimals and Percent Increase Problem.

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NCETM – Linking Fractions, Decimals and Percentages: A series of video lessons aimed at years 5 and 6

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Happy Numbers – Decimal Fractions: A series of lessons and activities exploring decimals to thousandths and operations involving the same. Work through the activities in Modules 1, 2 and 4.

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Maths Frame – Empty Number Line: Practice placing decimal numbers (tenths and hundredths) in the correct position; choose 0-1 in tenths or hundredths initially and then move to the next levels to challenge yourself. 

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Hit the Button: a great site for practicing quick-fire questions; options include Number Bonds (make 1 and make 10 with numbers to 1 decimal place), Doubles (to 10, 1 decimal place) and Halves (to 10, 1 decimal place).

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Rocket Rounding: A multiple choice game with options to round decimals to the nearest whole number. Start with the easier option of having a number line and then try to play the other more difficult option, no number line.

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Battleship Numberline: Can you blow up the enemy submarines? This game starts very easy, where you must click the correct fraction on the number line, but then the game progresses in difficulty as the player must work out where a given fraction would be placed on the blank number line. Choose the decimals game. 

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I Know It! – Decimals & Percent: Scroll down to Fractions-Decimals-Percent (Fifth Grade) to do any of those activities. There are also more decimal activities spread throughout the Place Value, Addition, Subtraction, Multiplication and Division sections. 

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Splash Learn – Decimals: An assortment of decimal games aimed at Fifth Grade

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Decimal Games & Percentage Games: An assortment of games using numbers of various sizes. Fifth and Sixth class should do the games up to 3 decimal places.

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That Quiz: Each of these quizzes have lots of options, on the left hand side, that can be changed to suit the ability of the child. Each time do the set 10 questions, if you get 10 or 9 correct, go up a level; if not stay at that level. Choose from Identify to identify and order decimals (choose decimal options for both on left hand side), Arithmetic for various calculations involving decimals and/or percent (choose desired options on left hand side), Inequalities for comparing decimals, percentages and/or fractions and Reduce for converting decimals and percentages to an alternative form. 

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Decimals and Percents: a selection of games from ixl.com. You can do a number of free quizzes each day without having a subscription. (Please note that the class levels given do not always align accurately with the content of the Irish Primary Curriculum)

Dear Family, your Operation Maths guide to Directed Numbers

Dear Family, below is a brief guide to understanding the topic of directed numbers (fifth and sixth classes only), as well as some practical suggestions as to how you might support your children’s understanding at home. Also below, are a series of links to digital resources that will help both the children, and you, learn more about directed numbers.

Understanding Directed Numbers

Directed Numbers are numbers with both size and direction; one direction is positive, and the other is negative. For example, temperature is typically described in a number of degrees either above zero (positive values) or below zero (negative values). Positive and negative numbers are also referred to as integers.

In Operation Maths, the children are first introduced to directed numbers in fifth class, where the focus is on the children appreciating where directed numbers can be encountered in real life, for example:

• Temperature
• Bank statements/ money accounts: having money is shown as positive (+) and owing money or overdrafts are shown as negative (-)
• Elevations above and below sea level
• Floors below the ground floor in a large building are often labeled as -1, -2 etc
• Golf scores are written as above and below par
• Goal difference in soccer league tables
• Depths in a swimming pool

In school, the children are encouraged to use the words positive and negative, rather than plus and minus; for example for the value -6 we should say negative six rather than minus six. This is particularly important for when the children start adding positive and negative numbers (in Operation Maths 6): for example (–3) + (+9) should be read as ‘negative three add/plus positive nine’ rather than ‘minus 3 plus plus 9’. It is also important that the children recognise that positive numbers can be written either with, or without, the positive sign, therefore we can assume that any number, without a sign, is positive.

Practical Suggestions for all Children

• Draw your child’s attention to wherever they or you encounter directed numbers (see above for possible examples).
• If your child is having difficulty visualising, comparing, ordering etc directed numbers, encourage them to think of a real example. One of the most-relatable of these is that of temperatures and the thermometer. Look at a real thermometer or use an online virtual example such as this one.
• As explained above, encourage your child to use the words positive and negative, rather than plus and minus, when describing directed numbers.

Digital Resources for Fifth and Sixth Classes

Integers: Video lesson that introduces integers (positive and negative numbers) and where they occur in real life

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Mashup Math – Elevation above or below sea-level: A video lesson that explores elevation as examples of positive and negative numbers.

 

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Negative Numbers: A series of video lessons from White Rose Maths, including Introducing Negative Numbers (Year 4), Negative Numbers (Year 4), Negative Numbers (Year 5), Negative Numbers in Context (Year 6), Negative Numbers (Year 6), Add and Subtract Integers (Year 6).

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Khan Academy Negative Numbers: A series of videos and practice questions exploring negative numbers. Afterwards, for more of a challenge, look at Integers and Whole Numbers. You can also register for a free Khan Academy account to record your progress and explore other topics/grades. 

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Maths Frame – Empty Number Line: Practice placing positive and negative integers in the correct position; choose -5 to 5 initially and then move to the next levels to challenge yourself. 

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What is the Temperature? Identify the temperature shown on the thermometers. A way to practice directed numbers in a real-life context. Includes values above and below zero, and has options for various ranges.

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Caterpillar Ordering: Choose Ordering and then -10 to 10 to order integers.

 

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Coconut Ordering: Hit the numbers in order of size. Select ‘numbers’ and then choose from numbers from -10 to 10 to order integers.

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Number Lines in Disguise: A challenge and interactive game (scroll down) from NRICH; Can you work out the number marked by the dot? Includes positive and negative numbers.

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That Quiz: Inequalities for comparing numbers, Arithmetic for addition calculations involving directed numbers and Number Line for identifying numbers by their position. In each of these activities there is the option to include negative numbers along with positive; just make sure the the “negative” option is selected on the left hand side.

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Number Line App: This virtual tool can be used to explore the position of values on a number line,including positive and negative numbers; also to model addition and subtraction involving positive and negative numbers.

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Directed Numbers Counters: These double sided counters can be used to model addition and subtraction involving positive and negative numbers (ensure that the “sign” option is ticked).

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Integers (Directed Numbers): a selection of practice games from ixl.com. You can do a number of free quizzes each day without having a subscription. Start with the second class games and work up through the activities.

 

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Integers: Practice games from Math Games. Choose your class level.

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